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 A168677 Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4. 2
 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1, 1, 1, 5, 1, 1, 1, 9, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It appears that the sequence is periodic with period (1,1,1,5,1,1,1,9) of length 8. LINKS Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1). FORMULA a(n)=(1/56)*{-51*(n mod 8)+5*[(n+1) mod 8]+5*[(n+2) mod 8]+33*[(n+3) mod 8]-23*[(n+4) mod 8]+5*[(n+5) mod 8]+5*[(n+6) mod 8]+61*[(n+7) mod 8]}, with n>=1 [From Paolo P. Lava, Dec 14 2009] EXAMPLE Assume that a(1) - a(7) have been determined as {1,1,1,5,1,1,1}. Then a(8)=1 gives consecutive terms 1,1,1,1, summing to 4; a(8)=2 gives 1+1+2=4; ... etc...; a(8)=8 gives 5+1+1+1+8=16; but a(8)=9 is ok, giving no sum of consecutive terms equalling 4,16,64,... . MATHEMATICA LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 5, 1, 1, 1, 9}, 105] (* Ray Chandler, Aug 25 2015 *) CROSSREFS Sequence in context: A066504 A292771 A322837 * A140210 A010130 A206773 Adjacent sequences:  A168674 A168675 A168676 * A168678 A168679 A168680 KEYWORD nonn AUTHOR John W. Layman, Dec 02 2009 STATUS approved

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Last modified March 28 10:32 EDT 2020. Contains 333083 sequences. (Running on oeis4.)